Bernie Sanders admitted Thursday that it will be difficult for his campaign to win at the Democratic presidential convention if he arrives in Philadelphia this July with fewer delegates than front-runner Hillary Clinton.

The Vermont senator spoke with NBC News Thursday in his first interview since Tuesday's loss in the New York primary, and had a less optimistic tone than normal.

Correspondent Andrea Mitchell asked Sanders if he would concede if his campaign did not have the majority by June 7, the day of California's primary.

"Look, if we do not have a majority, it's going to be hard for us to win. The only ... fact that I think remains uncertain is if we continue to be running significantly stronger than she is against Donald Trump, or whoever the Republican nominee will be. I think that's a factor," Sanders said in an excerpt from the interview, which will air Friday on MSNBC.

The next Democratic primaries are scheduled for April 26 and will take place in Rhode Island, Connecticut, Pennsylvania, Maryland and Delaware.