The official Syrian Arab News Agency (Sana) did not elaborate on the training discussed in the talks between Said Siam, Hamas's interior minister, and his Syrian counterpart, Bassam Abdel Majid.
Siam, who controls the interior ministry troops who fought deadly gun battles with Abbas loyalists on the streets of Gaza earlier this month, arrived in Damascus on Friday and was due to leave on Sunday.
This month's violence further complicated troubled talks between Hamas and Abbas's Fatah faction on forming a national unity government acceptable to Western donors.
Separately, Egypt, which has been attempting to help broker a deal, sent Omar Suleiman, it's intelligence chief, to Damascus on Saturday for a meeting with Bashar al-Assad, the Syrian president, Sana reported.
Fatah leader Faruq Qaddumi, who runs the Palestine Liberation Organisation's Tunis-based political department, was also in Damascus on Saturday for talks with Walid Muallem, the Syrian foreign minister.
Syria "is in favour of dialogue between the Palestinian factions and backs the formation of a national unity government encompassing all the different Palestinian groups," Sana quoted Muallem as saying.
Qaddumi said the Palestinians were seeking to "put an end to the [Israeli] occupation, guarantee the right of return [of Palestinian refugees] and establish an independent state".
On Friday, Qaddumi met exiled Palestinian leaders including Hamas political supremo Khaled Meshaal.
The Hamas-led government has faced a Western political and financial boycott since it took power in March over its refusal to foreswear violence or recognise Israel and past peace deals.
Al-Assad and Moratinos (R) held
talks in Damascus on Saturday
Abbas has been pressing the Islamists to agree to a unity government with a platform that will allow Western donors to end their damaging aid suspension, but they have so far resisted.
In other news, the official Syrian news agency said al-Assad and Miguel Angel Moratinos, Spain's foreign minister, met in Damascus on Saturday and discussed conditions leading to "a relaunch of the Middle East peace process" during talks.
The Syrian president and Moratinos discussed "recent developments in the region, as well as the friendly ties between Spain and Syria".
The two men also examined "the manner in which the European Union views a relaunch of the peace process", Sana said.
It quoted Moratinos as saying "Syria plays an essential role in the peace process and in stability" in the Middle East.