Shaikh Hamad was speaking in Doha, the Qatari capital, on Monday after talks with Hosni Mubarak, the visiting Egyptian president.
"Hamas came [to power] through elections that might be the most transparent polls in the Arab world," said the Qatari amir, whose government has put off until later this year at the earliest the emirate's first ever elections to a consultative assembly.
"That is why we should support Hamas in this period," he said in comments broadcast by Aljazeera.
"As for us in Qatar, we will continue to support them [Palestinians] in projects like industry and hospitals."
Qatar had already called upon the international community earlier in February to respect the will of the Palestinian people following Hamas's sweeping election victory.
The Egyptian president urged the Palestinian Authority's donors not to cut back on aid in response to the results of the election.
"This support is for the Palestinian citizen. If this citizen does not find food and could not raise his kids ... he will turn into an extremist"
Mubarak warned: "This support is for the Palestinian citizen. If this citizen does not find food and could not raise his kids ... he will turn into an extremist."
The Egyptian leader, who is on a Gulf tour, later left for Kuwait.
Along with the European Union, the United States has threatened to cut funding to the Palestinian Authority if Hamas does not radically alter its political platform - committing itself to non-violence, recognising Israel and past international agreements - before forming a new government.