A rift over the proposed southern border wall emerged Tuesday between Congressman Michael Capuano and his challenger in the Democratic primary, Boston City Councillor Ayanna Pressley.

Neither Capuano nor Pressley supports a wall on the southern border that President Trump has championed, but Capuano indicated he would be more open to the idea if it meant achieving some of his immigration priorities.

“I got to be honest. Look, I don’t care about a wall one way or the other. It is a nothing issue to me,” Capuano told business leaders on Tuesday morning. “It’s a stupid idea. It’s a complete and total waste of money, but if he needs his political victory to some extent, I’m not going to give him $25 billion, but I’d give him something to play and say, ‘Oh look my wall,’ as long as he gave us real immigration reform so we don’t have to play this game again.”

Pressley, who planned to officially launch her campaign against the Somerville Democrat at an event in Cambridge on Tuesday night, said she wouldn’t support any funding for the wall.

“Around many issues, I have been and will continue to be willing to work with many diverse groups. When it comes to protecting the most vulnerable among us, however, there can be no mistake: we must ensure that we don’t spend a penny on our President’s delusional border wall, and that at-risk communities in the district and across the country are protected from the bigoted policies coming from the Trump administration,” Pressley said in a statement responding to the congressman’s comments.

Launched from the mayoralty in Somerville’s City Hall to the US Capitol via a 10-way Democratic primary in 1998, Capuano is facing his first contested primary for the seat since he won it two decades ago.

There has so far been little separation on the issues between Capuano and his challenger, who became the first black woman elected to the Boston City Council in 2009. Both approach most political decisions from the liberal left.

During his Tuesday morning event with the New England Council, Capuano said he thinks it is “immoral” to use “dreamers” – who were brought to the country illegally as children – as leverage in legislative maneuvering. Trump last year rescinded President Barack Obama’s policy of administratively giving dreamers official sanction to remain in the country and the president also called for Congress to take action on the issue.

Pressley also voiced support for dreamers in her statement Tuesday, saying, “All good Democrats should care about fighting for justice for our dreamers.”

After Democrats and Republicans in Congress came to loggerheads over the dreamers and other issues in January, resulting in a partial government shutdown, the leaders of both the US House and Senate have indicated a willingness to take up a major immigration bill. The Senate began its debate this week.

“I think it would be great to do some kind of comprehensive immigration reform. If they really do it, I think it stands the chance of being bipartisan in the true sense of the word. But we’ll see,” Capuano told reporters on Tuesday. “A Senate bill came over a few years ago that they wouldn’t even put on the floor of the House. So we’ll see. Hope springs eternal. I actually think that immigration is one of the things that maybe we can work together on if they want to, but it’s also something that they can demagogue as well.”

Asked about how Trump would factor into November’s elections around the country, Capuano quipped, “I’ve invited President Trump to come in and endorse my opponent.”