This post has been updated.

President Obama and House Budget Committee Chairman Paul Ryan (R-Wis.) dined on lentil vegetable soup and broiled sea bass served with a roasted vegetable ragu at the White House on Thursday as the president continues a charm offensive with Republican lawmakers.

Obama had a "constructive discussion" with both Ryan and Rep. Chris Van Hollen (Md.), the Budget Committee's top Democrat, according to a White House official who was not authorized to speak to the media.

Topics included tackling the deficit and the president's proposal to replace the sequester with a deficit reduction package that includes tax increases, the official said. Obama "expressed his desire to continue a dialogue with them in the weeks ahead."

The meeting comes after Obama had dinner with 12 Republican senators Wednesday night at the Jefferson Hotel. The president picked up the tab personally and some of the senators emerged from the two-hour meal voicing optimism about reaching a long-term deal to reduce the federal deficit.

The meetings mark Obama's most intense courtship of Republicans since the early days of his presidency and follow more than two years of failed negotiations between him and House Speaker John A. Boehner (R-Ohio).

Ryan, the GOP's 2012 vice presidential nominee and the House's top fiscal guru, holds the keys to any bipartisan budget deal. He plans to introduce a new budget later this month, which is expected to be starkly different than the Democratic budget proposal that Senate Budget committee Chairman Patty Murray (D-Wash.) will unveil.

The budget process could become the forum for producing a so-called grand bargain this summer, when Congress will have to decide whether to raise the federal government's borrowing limit.

Rachel Weiner contributed to this report.