"We have supported all the precautionary measures taken by the Egyptian authorities to close the tunnels and stop the trafficking of arms and the passage of people between Gaza and the Sinai," Abbas said in an interview with Egyptian magazine Al-Ahram Al-Arabi due to be published on Saturday, extracts of which were published by MENA news agency.
"We will continue to support any measure protecting Egypt from danger," Abbas was quoted as saying.
Since the 2013 ouster of Islamist president Mohamed Morsi by the Egyptian army, the country's new authorities have accused Morsi's Muslim Brotherhood of conspiring with Hamas.
The Egyptian military has stepped up the destruction of tunnels from Gaza that it says are used by the Palestinian Islamist movement to smuggle arms, food and money.
The army says it has destroyed more than 1,600 such tunnels since Morsi's ouster.
Signup to our newsletter and follow us on Facebook and Twitter!
Egypt has also begun setting up a buffer zone along its border with the Gaza Strip, which will see hundreds of homes demolished, in order to prevent militant infiltration and arms smuggling.
Bitter rivals Hamas, the de facto rulers of Gaza, and Abbas's Fatah movement, which dominates the West Bank-based Palestinian Authority, agreed on a national unity government earlier this year but reconciliation efforts have repeatedly hit stumbling blocks.
Cairo also suspects Hamas militants of helping jihadists carry out a spate of deadly attacks against Egyptian security forces in the Sinai Peninsula recently.
In one such attack in late October, at least 30 soldiers were killed in a suicide bombing in the Sinai Peninsula.
"If it is proved that Hamas members are implicated in terrorist attacks against Egypt, it has the right to go after them and punish them," Abbas said, according to MENA.
Jihadists say they are taking revenge against a police crackdown on Morsi supporters that has left more than 1,400 dead.