The European Union is ready to help the Palestinian Authority "build an economy and civil society", Moratinos told reporters after talks with Abbas and Palestinian Prime Minister Ahmad Qureia in Gaza City on Tuesday.
Qureia said issues linked to Israel's departure from the territory after a 38-year occupation have yet to be resolved, notably the fate of the Rafah border terminal between Gaza and Egypt.
"The most important unresolved question is the crossing points, particularly Rafah. We have heard various proposals that we think are impractical, but we hope to close this matter soon thanks to international and Egyptian efforts," he said.
The Palestinians demand Israel turn over full control over the Rafah crossing, but Israel insists it wants to monitor all goods crossing into Gaza by moving the terminal farther south where the Gaza, Egyptian and Israeli borders converge.
A senior Israeli official said on Monday that a compromise on allowing civilians and goods in and out of Gaza could be reached in the next few days.
The Palestinians have suggested a third party, possibly European, could help oversee the checks of civilians crossing into Rafah.
Moratinos also met his Palestinian counterpart Nasser al-Qidwa, who insisted that the Rafah terminal be solely under "Egyptian-Palestinian control without any Israeli presence".
Al-Qidwa reiterated that the legal status of the Gaza Strip as an occupied territory would remain the same even after the departure of the last Israeli troops from the territory in the middle of the month.
"The most important unresolved question is the crossing points, particularly Rafah"
Palestinian prime minister
The Palestinians have argued that Israel will effectively remain an occupying power until they have full freedom of movement in and out of Gaza by land, sea and air.
Moratinos, a former EU special envoy to the region, is paying his first visit to the Gaza Strip since Israel began its withdrawal from the territory two weeks ago.
His French counterpart Philippe Douste-Blazy is also to arrive late on Tuesday ahead of talks with Palestinian leaders, after an EU-led momentum that began with a visit last week by the bloc's foreign policy chief, Javier Solana.