UPDATE 1-Indonesia president wants to wrap up Freeport talks by end-April

* Government plans to acquire Rio's Grasberg interest -minister

* Freeport Indonesia says negotiations have been constructive (Adds comment from Freeport Indonesia)

JAKARTA, March 6 (Reuters) - Indonesia President Joko Widodo has instructed his administration to complete negotiations over the purchase of a majority stake in Freeport-McMoRan Inc's local unit by the end of April, a cabinet minister said on Monday.

"According to the president, it should be wrapped up before the end of April, valuation and all," Energy Minister Ignasius Jonan told reporters.

The government, through a state-owned company, will buy the shares in PT Freeport Indonesia (PTFI) at "a reasonable price," including by acquiring Rio Tinto's participating interest in the massive Grasberg mine and converting it into shares, he said.

PTFI spokesman Riza Pratama told Reuters by text message that negotiations between both sides had been constructive. "Hopefully we'll reach an agreement soon," he said.

Rio Tinto did not immediately respond to emailed requests for comment.

Freeport in January said it was edging closer to a permit deal with Indonesia for Grasberg, the world's second-biggest copper mine, but the miner cautioned it had not struck any formal agreements.

Rio has a 40 percent interest in PTFI's Grasberg contract, which entitles it to a 40 percent share of all production after 2022. Rio has held talks with Indonesia about a possible exit to the venture.

There have been few signs of progress since last August, when Freeport promised to divest a 51-percent stake in Grasberg to the Indonesian government in exchange for long-term operating rights. The government currently owns a less-than-10 percent stake in Freeport Indonesia.

The valuation of the stake it plans to acquire has been a sticking point in negotiations. (Reporting by Wilda Asmarini Writing by Gayatri Suroyo and Fergus Jensen Editing by Mark Potter and Kenneth Maxwell)