Zapatero, whose country holds the European Union's rotating presidency, said Foreign Minister Miguel Angel Moratinos would propose to EU counterparts at a meeting on Monday that the 27-nation bloc "clearly declare itself in favor of ending the blockade of the Gaza Strip."
The ministers are set to discuss a "plan for lifting the blockade" in order to "ensure the entry" of humanitarian aid and commercial goods.
Zapatero added that his government hoped that "with the help of the American president, Barack Obama, we will be able to create a schedule for direct talks and opening of dialogue between Israel and the Palestinians".
Abbas arrived in Europe after a visit to the US, during which he met with President Barack Obama and Secretary of State Hillary Clinton.
On Thursday Abbas warned US officials that the concept of a two-state solution to end the conflict between Israel and the Palestinians "is beginning to erode."
"I would like to express concern that the situation is very difficult," he said in remarks at a Washington think tank. "The concept of a Palestinian state ... with an Israeli state, I fear, is beginning to erode," he said.
Regarding the IDF raid on a Gaza-bound aid flotilla he said, "There are behaviors that the Israelis should
desist from in order to present themselves in a positive way. The Arab people are not against peace and neither are the Muslim people."
From Madrid the Palestinian president is scheduled to fly to Paris, where he will meet with President Nicolas Sarkozy. The two intend to discuss negotiations with Israel as well as the flotilla incident.