By David Lawder and George Georgiopoulos

ATHENS (Reuters) - U.S. Treasury Secretary Jack Lew on Thursday urged Greek officials to make more progress on budget and economic reforms to help unlock European debt relief and boost growth in the struggling economy.

Following a meeting with Greek Finance Minister Euclid Tsakalotos in Athens, Lew said Greece needed "to make headway on the next set of milestones due in October, including by following through on privatisation plans and moving forward with critical financial sector reforms."

Athens and its euro zone partners, financing its third bailout since 2010, are trying to reach an agreement with the International Monetary Fund, which has yet to commit to taking part in funding the loan package of up to 86 billion euros.

Lew said it was important for debt restructuring to be part of an overall plan to get Greece out of the crisis, noting that the IMF needs to remain part of the discussions.

"The IMF has been a very helpful partner in the process ... and the work that has been done to bring progress forward," Lew said.

His view echoed EU Commissioner Pierre Moscovici, who said earlier this week during a visit to Athens that it is in the interest of all parties for the IMF to stay fully on board.

Greek Finance Minister Euclid Tsakalotos said that following the bailout agreement clinched in May last year, all sides are now discussing "technical details on how and when and not whether (debt restructuring) is necessary."

Lew told reporters reform progress was important so that European leaders can begin talks with the IMF on the timing and details of Greek debt relief, which euro zone finance ministers committed to pursuing in May.

He said there were multiple ways to make Greece's 300-billion debt burden more sustainable, urging all sides to agree on an outcome that produces long-term clarity for investors.

"I'm not going to take a hard view on where Greece and institutions should end up. Except that in the end, it has to work," he said.

"Putting Greece's debt on a sustainable path is critical to Greece's long-term economic health and I encourage all parties to be flexible to successfully conclude this fall's negotiations," Lew said.

The IMF has argued that Greece's bailout target for a primary budget surplus of 3.5 percent of gross domestic product beyond 2018 is hard to achieve and has pushed for softer fiscal targets to take part in financing the third bailout.

Asked whether fiscal targets should be lowered, Lew would not commit to specifics, saying it is something that Athens will need to work out with its partners in the long run.

(Reporting by David Lawder and George Georgiopoulos; Editing by Catherine Evans and Alexandra Hudson)