Abbas met with President Leonel Fernandez yesterday and was also to address the Dominican Congress over the quest for statehood, which he formally presented to UN Secretary General Ban Ki-moon on September 23.
"We don't hesitate to recognize the legitimate right of Palestine to be recognized as a free, independent and sovereign State," Fernandez said, underlining that his country also had "excellent diplomatic, commercial and cultural relations with Israel."
Abbas replied: "You're not big militarily but you're big in faith, peace and solidarity with the Palestinian people."
The Palestinian president is also due to travel to El Salvador and Colombia, where President Juan Manuel Santos has already pledged to abstain in any UN Security Council vote.
Colombia, a close ally of Washington, is a non-permanent member of the 15-member Security Council, which is expected to vote on the bid in the coming weeks.
The move is strongly opposed by both Israel and the United States, which say a Palestinian state can only emerge through bilateral negotiations.
Six Security Council members -- Brazil, China, India, Lebanon, Russia and South Africa -- have publicly indicated their backing for the Palestinian bid.