(Adds details, background)

DUBAI, April 30 (Reuters) - Moderate candidates allied to President Hassan Rouhani came out strongest in a second round of parliamentary elections in Iran, unofficial results showed on Saturday, but they appeared unlikely to win an overall majority.

The results, if confirmed, suggest Iran's next parliament will be more supportive of Rouhani's drive for economic reforms, but conservatives will remain a powerful force and could limit the prospects for social change.

Iranians voted on Friday for 68 seats where no candidate had won decisively in the first round, held in February. Rouhani's allies made significant gains in the first round, ending conservative dominance of the 290-seat assembly.

Unofficial results compiled by Iranian news agencies suggested moderate candidates won around 30 of the 68 seats in the second round, with the rest split between conservatives and independents.

An unofficial Reuters tally of first-round results showed moderates won about 90 seats, conservatives 112, and independents 29. The figures are approximate because Iran does not have rigid party affiliations and some candidates were backed by both camps.

If Saturday's unofficial results are borne out, neither the moderates nor the conservatives will have a majority in the next parliament, and independent candidates will determine the balance of power.

Rouhani, who came to power in 2013 on a pledge to end his country's global isolation, has seen his support increase since reaching a nuclear deal with world powers last year, which resulted in the lifting of international sanctions in January.

(Reporting by Sam Wilkin; Editing by Gareth Jones) ((sam.wilkin@thomsonreuters.com; +971 4453 6873; Twitter @MrSamWilkin;))

Keywords: IRAN ELECTION/