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But in another sign both sides are talking past each other, Mr. Obama on Monday once again called for House Republicans to specify which parts of his package they would be willing to accept.

House Republicans said they’ve done so, pointing to a Sept. 16 memo from their leaders to rank-and-file House members laying out areas of agreement, including extending business-expense write-offs, expanding federal infrastructure spending, offering incentives to businesses that hire veterans and working on more middle-class tax cuts.

They also pointed to three free-trade agreements, which Mr. Obama submitted to Congress on Monday, as another area of cooperation.

The memo, though, rejected Mr. Obama’s proposed tax increases and his pledge of more money to help states and localities avoid layoffs of public employees.

Seeking to add their own proposals to the mix, Republican House leaders on Monday sent the president a letter outlining the two measures the House will vote on this week, to delay the Environmental Protection Agency from implementing new regulations Republicans say would cost millions in compliance costs for employers.

“It is our hope that in the spirit of putting country before party, you will call on the Senate to follow the House in passing these measures, and commit to signing them into law should they reach your desk,” they told the president.

White House spokesman Jay Carney told reporters Monday that Mr. Obama would be willing to consider signing some pieces of his overall, if Congress were to pass them piecemeal.

Stephen Dinan contributed to this article.