"I’m still committed, but obviously this is the single most important thing on the agenda," the president told journalists after his meeting with congressional leaders on the debt ceiling.
The president added, however, that it was "not likely" his trip would be canceled, but it was possible.
"If somehow we got down to the wire and we still hadn’t resolved this, and the due date was a matter of when I was supposed to be away, I would not go," Biden said. "I would stay until this gets finished."
Earlier Tuesday, Biden met with congressional leaders at the White House to negotiate raising the US debt limit to avoid a possible default in June. Following the meeting, Biden said it was productive and the United States reiterated claims that the US would not default on its debt obligations.
US House Speaker Kevin McCarthy said that he did not see "any new movement" toward resolving the issue, adding he hopes Biden "would be willing to negotiate for the next two weeks so we could actually solve this problem and not take America on the brink."
US Senate Minority Leader Mitch McConnell said the US will not default on its debt obligations.
Biden's next meeting with congressional leaders on the issue of raising the US debt limit will be held on Friday.
Earlier in May, the US Treasury Department said the US government will likely begin defaulting on its debt by June 1 if the congressional limit on the country's debt servicing is not raised by then.
In late April, House Republicans passed legislation to raise the debt ceiling in exchange for cuts in federal spending and other measures to reduce the deficit. However, Senate Democrats and Biden rejected the proposal, saying it had no chance of becoming law. Inversely, McCarthy said a "no-strings-attached" debt limit increase would not pass the lower chamber of Congress.