The invitation comes after an investigation commissioned by Al-Jazeera news channel found elevated levels of the radioactive substance polonium on some of Arafat's belongings, suggesting the leader could have been poisoned.
"President (Mahmud) Abbas ordered one of his medical advisors to communicate immediately with the experts at the Swiss institute who tested Arafat's clothes and request they come immediately to Ramallah to take samples from Arafat's body," Saeb Erakat told AFP late on Sunday evening.
He added that Abbas hoped further tests by the experts "will reveal the real cause for Arafat's death."
Polonium, which is highly toxic, was used to kill Russian former spy turned Kremlin critic Alexander Litvinenko, who died in 2006 after drinking tea laced with the substance at a London restaurant.
The Al-Jazeera investigation, broadcast last week, centred around the testing of some of Arafat's belongings, which had been handed to his wife Suha by the Paris hospital where he died in 2004.
Suha Arafat gave Al-Jazeera permission to take possession of the items, which included clothing Arafat wore in the days before he died aged 75, and hand them over for specialist testing.
Among the experts consulted by the news channel were specialists at the Institute of Radiation Physics at Switzerland's University of Lausanne, which discovered the elevated levels of non-naturally occurring polonium.
Francois Bochud, head of the institute, told the news channel that tests had revealed "significant polonium" in samples that included Arafat's hair and blood.
But to confirm the theory that the Palestinian leader was poisoned by polonium it would be necessary to exhume and analyse Arafat's remains, Bochud said.
"If (Suha Arafat) really wants to know what happened to her husband (we need) to find a sample -- I mean, an exhumation... should provide us with a sample that should have a very high quantity of polonium if he was poisoned," he said.
Suha Arafat has already said she would seek an exhumation to allow specialists to take additional samples for testing, and the Palestinian leadership has said it would be willing to allow exhumation if Arafat's family agreed.
Many Palestinians believe Arafat was poisoned by Israel, which has denied the allegations, accusing Suha Arafat and Palestinian officials of covering up the real reasons for the former leader's death.