The three were joined yesterday in Amman by Palestinian parliamentary speaker Rawhi Fattuh.
All four men today were authorized to see Arafat at France's Percy military hospital near Paris.
Speaking to reporters after the brief visit, Abbas described the condition of the veteran Palestinian leader as "very serious."
Shaath was quoted as saying Arafat was alive and on life-support. He said Arafat has been in a coma since 3 November.
Shaath said no specific illness has been established. But he said Arafat is not suffering from cancer, and that his brain, heart, and lungs are still functioning.
Earlier today, Percy hospital spokesman Colonel Christian Estripeau said Arafat's health had suddenly deteriorated.
"The state of health of President Yasser Arafat has worsened during the night of the 8th to 9th November 2004," Estripeau said. "The comatose state that had led to his admission into a recovery unit is deeper this morning. That marks a significant step toward an evolution which cannot yet be determined."
In Ramallah today, Palestinian cabinet minister Saeb Erekat denied reports that the 75-year-old leader was dead. Earlier he had described Arafat's condition as critical.
"We have received reports that President Arafat's condition has deteriorated this morning. Our prayers are with him," Erekat said.
The Palestinian delegates were able to visit Arafat despite earlier opposition from Arafat's wife Suha.
In a telephone interview with the Al-Jazeera Arab television network, Suha Arafat 8 November accused her husband's top lieutenants of trying to "bury him alive."
Suha Arafat's comments initially prompted the Palestinian delegates to scrap plans to visit Paris. But, yielding to pressure from Leila Shahid, the Palestinian envoy to France, they eventually changed their minds and proceeded to the French capital through Amman.
But there may be more to the delegation's decision to go ahead with their visit.
French Foreign Minister Michel Barnier said today that he and President Jacques Chirac expected to hold "personal and political" consultations with the Palestinian envoys.
As a cosponsor of the Middle East peace process, the European Union is focused on Arafat's succession and has started discreet talks with the Palestinian leadership over who is likely to take over. Spain's Foreign Minister Miguel Angel Moratinos flew to Damascus over the weekend to inquire about Arafat's possible successor.
The Palestinian delegates met with Barnier before visiting Arafat. They are scheduled to hold talks with Chirac later today before flying back to Ramallah.