Barack Obama spoke with David Cameron by phone to discuss the fight against so-called Islamic State in Syria on Friday.
The US President welcomed the outcome of Wednesday's vote in the House of Commons authorising the RAF to carry out airstrikes against the terror group, a White House spokesman said.
President Obama "expressed his appreciation" that British air forces had joined the coalition in Syria.
"The leaders discussed further steps that can be taken to degrade and destroy ISIL, and reiterated that all countries are welcome to join the existing coalition, if their political and military objectives in Syria are consistent with those of the Coalition," the White House spokesman said.
"They also discussed ways to further bolster our already robust counterterrorism cooperation, and the President, on behalf of the American people, accepted the Prime Minister's condolences for the loss of life in the San Bernardino shootings this week."
The shadow chancellor warned it could foster another generation of militants determined to commit a Paris-style terror attack.
The Defence Secretary has warned the RAF that the fight against Islamic State will not be short or simple.
Officers were posted outside the constituency office of Neil Coyle, the Labour MP for Bermondsey & Old Southwark.