(CNN) A day after congressional Democrats declined to meet with President Donald Trump over ending the government shutdown, at least seven House Democrats attended a White House meeting Wednesday aimed at reopening the government that has been partially closed for more than three weeks.

Democratic Reps. Josh Gottheimer of New Jersey, Thomas Suozzi of New York, Vincente Gonzalez of Texas, Anthony Brindisi of New York, Dean Phillips of Minnesota, Max Rose of New York and Abigail Spanberger of Virginia attended the midday White House meeting in the Situation Room. The lawmakers are not part of Democratic leadership, which has been leading congressional negotiations, and are rank-and-file members mostly hailing from more moderate congressional districts.

Trump is trying to get congressional Democrats to agree to as much as $5 billion in additional funding for the President's signature campaign promise of a wall along the US border with Mexico. D emocratic leaders have not budged on that issue, leading White House negotiators to try to target moderate members to put pressure on House Speaker Nancy Pelosi and Senate Minority Leader Chuck Schumer.

It's unclear at this point if the Wednesday meeting will put daylight between the moderate members and leadership.

That group, in a statement released before the meeting, reiterated the position of Democratic leadership: that the government must be reopened before any negotiations on border security can commence.

Read More