|Some travellers in the US will have their temperatures checked for signs of a fever|
He said many relatives of the only known person to have died of the virus in America seemed to be out of danger.
Mr Obama said there were "modest signs" of progress in Liberia - the hardest-hit nation in West Africa.
The known death toll is now 4,877 - a rise of 322 since last week's report by the World Health Organization.
Most of the victims died in three West African nations - Liberia, Guinea and Sierra Leone.
In other developments:
- The WHO is meeting in Geneva to examine screening measures at borders and considering whether stricter travel regulations should be put in place
- First batches of an experimental vaccine against Ebola are due to arrive to Switzerland
- Doctors in Spain said a second round of tests showed Teresa Romero, who became the first person to contract Ebola outside West Africa, was completely clear of the virus
- A Cuban medical team has arrived in Liberia to join the fight against Ebola
- Doctors in the US say they no longer detect the virus in Texas nurse Amber Vinson, the second US to contract the virus from Liberian Thomas Duncan.