WASHINGTON — In his most comprehensive effort to assure wavering Democrats, President Obama wrote in a letter to Congress that the United States would unilaterally maintain economic pressure and deploy military options if needed to deter Iranian aggression, both during and beyond the proposed nuclear accord.

The Aug. 19 letter, obtained by The New York Times, is addressed to Representative Jerrold Nadler, Democrat of New York, but is also aimed at other Democrats with concerns about the deal. For Mr. Obama, it reflects steps the administration could take outside the agreement. The president has repeatedly said that the deal reached by Iran and six world powers cannot be changed.

While many of the promises have been made before by Mr. Obama, Secretary of State John Kerry and others, White House officials say the letter represents the first time that the president himself has compiled them under his name and in writing. It commits explicitly to establishing an office within the State Department to carry out the nuclear accord.

In addition, Representative Adam Schiff of California, the ranking Democrat on the House Intelligence Committee, said that the letter expanded assurances that sanctions lifted under the nuclear accord could be reimposed piece by piece, not all at once, to keep Iran in compliance. Mr. Obama’s pledge to use the multinational commission policing the accord to block Iranian procurement of nuclear-related technology is new, as is the president’s explicit pledge “to enhance the already intensive joint efforts” of the United States and Israel in the region, said Mr. Schiff, a supporter of the deal.

“Should Iran seek to dash toward a nuclear weapon, all of the options available to the United States — including the military option — will remain available through the life of the deal and beyond,” Mr. Obama wrote.

He pledged to increase missile defense funding for Israel, accelerate co-development of missile defense systems, and boost tunnel detection and mapping technologies. He also vowed to increase cooperation with Israel and Persian Gulf allies to counter Iran’s efforts to destabilize Yemen, its support for Hezbollah in Lebanon, and its efforts to preserve the government of President Bashar al-Assad in Syria.

The letter comes as supporters of the nuclear deal close in on the number of lawmakers they need to sustain a presidential veto of Republican-led efforts to block it. The announcements of support by moderate Democrats from Republican-leaning states, such as Senators Claire McCaskill of Missouri on Thursday and Joe Donnelly of Indiana on Wednesday, have changed the dynamic of the Iran debate. “This was not an easy call. It was a close call,” Ms. McCaskill said Thursday. “It’s wrong for anybody, including the president, to accuse those who don’t support this deal of bad faith or warmongering.”

With 26 Senate Democrats declaring their support for the accord, and five others leaning toward supporting it, it is becoming increasingly difficult for opponents of the deal in the Senate to find the 67 votes needed to override a veto.

Even some senior Republicans are looking beyond the September showdown to the accord’s implementation. “I’ve said from Day 1 it’s a heavy lift, and the administration has been effective with Democrats in saying it’s this deal or no deal,” said Senator Bob Corker of Tennessee, the Senate Foreign Relations Committee chairman working to kill the accord. “There’s going to have to be a regional follow-on now. This cannot be implemented in a vacuum because this will be our Middle East policy.”

The president and Democratic leaders are now pressing for a more convincing vote. Representative Nancy Pelosi of California, the minority leader, is coordinating efforts to secure enough Democratic support to sustain a veto, through “Dear colleague” letters from respected members and assurances from outside experts. A two-thirds vote to override is also required in the House, and if the vote falls short in either chamber, the agreement goes through.

“I need to have 146 to win,” Ms. Pelosi said in an interview. “Do I want more? Yes. I want more because I want this to be unifying.”

So far, only two Senate Democrats — Chuck Schumer of New York and Robert Menendez of New Jersey — have declared their opposition to the deal. That raises the possibility that a resolution of disapproval, to be voted on around Sept. 16, could fail to get the 60 votes needed to break a filibuster, ending any threat of a veto showdown.

Mr. Obama’s letter could solidify support. Of the 14 House and Senate Democrats who have come out against the deal, nine are from New York and New Jersey. Addressing Mr. Nadler

In a statement, Mr. Nadler, who represents a heavily Jewish district in Manhattan, said he raised “troubling” questions “about our ability to permanently stop Iran from developing a nuclear bomb, and our commitment to strengthening the U.S. strategic relationship with Israel, as well as Iran’s continued destabilizing influence through support of terrorism and other actions that threaten Israel’s security and the security of our other Middle East allies.”

“I am gratified that the president’s response satisfies a number of these concerns,” Mr. Nadler said in a statement.

Mr. Nadler plans to endorse the deal on Friday, according to sources familiar with his decision, who asked to speak anonymously because the congressman has not yet made a formal announcement.

Senator Chris Coons of Delaware, an influential Democrat on the Senate Foreign Relations Committee, said he and others had suggested to Mr. Obama and Vice President Joseph R. Biden Jr. ways that the administration could unilaterally address issues around the Iran nuclear accord without renegotiating it.

Those include interdiction of conventional weapons shipped from Iran, enforcement of sanctions placed on Iran for its support of terrorism and its abuse of human rights, and deterrents for other destabilizing or destructive acts around the world.

“This is not a one-day decision about one up-or-down vote,” said Mr. Coons, who is also undecided on whether to support the deal. “This is about what happens after the vote.”

Republicans pounced this week on an Associated Press report that confirmed a deal between the International Atomic Energy Agency and Iran that would let Iran conduct portions of the inspections themselves at the disputed military site of Parchin, where the I.A.E.A. suspects some nuclear weapons-related experiments may have been conducted years ago. “This side agreement shows that true verification is a sham, and it begs the question of what else the administration is keeping from Congress,” said Representative Kevin McCarthy of California, the House majority leader.

But that issue involved a longstanding effort by the I.A.E.A. to complete a report on past Iranian efforts to develop a nuclear weapon, an important part of the international effort to pressure Iran. It has little to do with verification of the nuclear accord between Iran and the United States, Britain, Germany, France, Russia and China. That verification regime is laid out in the actual nuclear accord and does not rely on Iran’s self-monitoring.

The issue surfaced last month at the first Senate hearings on the Iran deal, when Republican senators mocked the verification procedures as unacceptable even by National Football League standards.

The head of the I.A.E.A., Yukiya Amano, issued a statement Thursday saying the reports were “misleading.” He added: “I am disturbed by statements suggesting that the I.A.E.A. has given responsibility for nuclear inspections to Iran. Such statements misrepresent the way in which we will undertake this important verification work.” But because those agreements are confidential, he did not explain how the inspections would proceed.

On Thursday, The Associated Press published a transcript of the original draft agreement.

Mr. Corker said that by agreeing to the self-reporting procedures, the I.A.E.A. was laying down a dangerous precedent for any future disputes with Iran.

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