Hague, in Australia for high-level security talks, said he was in regular contact with the British embassy in Tunis and that the situation in the country was "still fluid".
"It is important the interim government there gets on with matters, quickly and decisively, and that they do so in accordance with their constitution and respecting human rights," he told a press conference in Sydney.
Tunisia on Monday unveiled a new government which promised unprecedented freedoms in the once tightly controlled country and said it would prepare to hold elections within six months.
Weeks of turmoil in the Arab state forced president Zine El Abidine Ben Ali to flee last week after 23 years in power and left 78 people dead.
"The elections that are now scheduled in our view should be free and fair elections and that should be clear to the world," Hague said.
The British foreign secretary refused to be drawn on whether the upheaval in Tunisia would trigger similar events elsewhere in the Arab world.
"I think it is possible to say that the situation in Tunisia would have been helped, the situation of the people of Tunisia would have been helped by more effective economic development and by a more open, flexible political system," Hague said.
"So other countries must draw their conclusions from that but it is still a developing situation and we must not rush to predict events elsewhere from what has happened in that particular country."
Australian Foreign Minister Kevin Rudd said he had discussed Tunisia with Hague and the implications of the unrest on the broader Arab world during their talks in Sydney.
While it was too early to make "substantive comments" on the situation, he said "the democracy deficit in a number of countries in that region" had been a reality for a long time.
"And it is a reality which needs to be addressed as well," Rudd said.