In a wide-ranging interview published over two days, Abbas expressed concern that "if the activists manage to enter the PA without any monitoring, there will be destructive consequences for the whole region.
"This is the first time I am talking about this issue. This is very dangerous," he said.
Abbas added that the PA did not have information showing that Hizbullah was operating in the territories.
The interview took place during Abbas recent visit to Yemen. The Palestinian leader discussed a number of issues including Hamas' elections victory, and Palestinian ties with Syria, Iran, the U.S., and the EU.
Abbas said he did not oppose Hamas establishing close ties with Syria and Iran, but stressed that Iran should not be a side to the conflict. Abbas added that ties with Syrian President Basher Assad were excellent, and that he had been invited to visit Damascus and Teheran.
The PA chairman was asked whether he received an official report about Iran financially supporting the Palestinian Authority, and his opinion of that support. In response, Abbas said: "I did not receive such a report, but I heard that Iran will help the Authority. If Iran wants to help, it is welcome. What is important is that the help will arrive to the Palestinian Authority. We won't pay any price in exchange for the aid. We have our stances and policies, and whoever wants to support us on that basis, we welcome that and thank them."
'I prefer to wait'
Regarding declarations by Hamas Politburo Chief Khaled Mashaal during his visit in Teheran, which included calls to wipe out Israel, Abbas said: "Hamas hasn't changed its language up to now, yet personally I believe that it will change its language. I prefer to wait."
Abbas also said that "it would be impossible for Hamas to reverse its stance a 180 degrees within a month. I see the visits of Hamas heads abroad as helpful and important. They express their views and listen to those of others, thereby formulating their opinions."
The PA chairman also denied rumors regarding his intentions to resign.
"The issue of my resignation is one big rumor. But the chair is not my goal and never was. The chair is a means, and therefore if I can get what I want through it, I'm willing to struggle for that that. However, if I get to a dead-end, and can't get what I want, I won't see any use in staying at the post," he said.
Referring to his predecessor, Yasser Arafat, Abbas said that "the case on the issue of his death will remain open until we investigate the truth."