"I expect them to do their job", he said, and consider the candidate as required by the US Constitution.
Scalia, a long-time conservative on the court, died on Saturday.
Leaders of the Republican-controlled Senate have said they would delay confirming any nomination until a new president is in power next year.
Republicans argue it should be up to the electorate to pick a president who can nominate the right candidate for the job.
Scalia's death leaves the court finely balanced with four judges appointed by Democratic presidents and four by Republican ones, so the new appointment would leave the court liberal or conservative leaning.
"The Constitution is clear about what is supposed to happen now, said Mr Obama, during a news conference at an economic summit in California for South-East Asian countries.
The president must nominate someone for the court and then it's up to the Senate to confirm or reject him or her, he said.
"There's no unwritten law that says that it can only be done on off years. That's not in the constitutional text."
The president vowed to announce his preferred candidate "in due course" and called on Washington to employ "basic fair play" to get it done.
In recent years, the court has made key rulings on gay marriage, abortion and Mr Obama's key healthcare legislation.
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