In an interview with Palestine TV while in the US, 82-year-old Abbas rejected reports he had been rushed to hospital during his visit.
“It was a suitable opportunity to be here to conduct some medical tests, and these tests have been conducted and now we left,” he said after leaving the hospital.
“Thank God all the results are positive and reassuring.”
The health of the longtime smoker has long been the subject of speculation, with no clear successor identified.
Abbas was in the US to meet with political allies amid a breakdown of communication with the US administration following President Donald Trump’s controversial recognition of Jerusalem as Israel’s capital.
The Palestinians, who see the eastern part of the city as the capital of their future state, have said the US has disqualified itself as a mediator in talks with Israel and cut political ties with the administration.
Trump is expected to propose a peace plan in the coming months.
Abbas has been in power since winning presidential elections in 2005.
He has remained in the role despite his initial mandate expiring as splits between the Palestinian factions have made fresh elections impossible.