Incoming House Speaker John Boehner said President Barack Obama called with congratulations for winning control of the House.
During what Mr Boehner described as a brief but pleasant midnight conversation, the two discussed working together on priorities for Americans.
Mr Boehner said he told the president that the people expect them to cut spending and create jobs.
Mr Boehner described the call in a statement.
Earlier in the evening, Mr Boehner and other Republicans said they were eager to work with Mr Obama – on their terms.
Republicans have said they want to cut $100bmn (€71bn) in the first year and try to roll back Mr Obama’s overhauls of health care and financial regulations.