The move is a first step towards setting up a satellite station similar to the one Hizb Allah runs in Lebanon, Hamas officials said on Monday.
The Al Aqsa Television station is being set up just weeks before Palestinians vote in parliamentary elections on 25 January. If it is up and running in time, it could help Hamas in its election campaign.
Hamas presents a serious challenge to the ruling Fatah party, which has led the Palestinian Authority since its establishment in 1994.
Mahmoud al-Bik, a Hamas official, said: "The first transmission tests for Al-Aqsa Television in Gaza began today."
For up to three months, the channel will broadcast news bulletins and political and social programmes, ahead of its official launch at a later date, he said.
Al-Bik said the channel would also inform voters about the candidates standing for Hamas in the elections, only the second ever to the Ram Allah-based parliament.
The station broadcast half an hour of readings from the Quran on Sunday, but nothing else due to technical difficulties.
During down times, a picture of the Al Aqsa Mosque in Jerusalem, one of Islam's holiest sites, fills the screen.
Once officially launched, Al Aqsa Television will be the first private station in Gaza. Hamas says it wants the station to be hi-tech and modern, not like the stodgy, state-run Arab stations.
Hizb Allah's Al Manar has reporters throughout the Middle East, including Israel, the West Bank and Gaza, who cover events on location. When Hizb Allah attacks Israeli targets, Al Manar often broadcasts images of the strike.
Hamas' Al Aqsa Television will seek to do similar things. The Hamas official said the station aims to carry the group's message to the Palestinian people and to the world.
Freedom of speech
Moheib Nawati, a political analyst in Gaza, said: "Politically and from a freedom of expression point of view, every party is entitled to have whichever medium it sees fit, to present its political programmes and promote them."
"The timing, I think, serves the election campaign and is in a way a form of early preparation for Hamas' attempt to control matters more, including presenting its political programmes after the elections," Nawati said.
"Politically and from a freedom of expression point of view, every party is entitled to have whichever medium it sees fit, to present its political programmes and promote them"
The group already broadcasts programmes on its Voice of Al-Aqsa radio. For an experimental period, the television will broadcast from 10am until 11pm. Now, with the group expanding into politics, it wants a TV station to effectively spread its new ideas, Nawati added.
Hamas is the second most powerful group in Palestine, gaining popularity for its military operations against the Israeli occupation and a network of social services.