UPDATE 1-Minnesota governor's veto of legislature budget constitutional -court

-court@ (Adds statement by Republican leaders, paragraph 7)

Sept 8 (Reuters) - The Minnesota Supreme Court said on Friday that Governor Mark Dayton's veto of funding for the state legislature was constitutional but it also ordered the two branches of government into mediation to resolve their dispute.

The high court cited doubts over the legislature's ability to continue functioning without funding as a reason for the order.

"The other branches should resolve these doubts through the political process. Thus far, they have not done so," the court said. "As a result, Minnesotans may soon be deprived of their constitutional right to three independent branches of government."

Minnesota's Democratic governor used his line-item veto in May to remove funding for the Republican-controlled state legislature in the fiscal 2018-2019 biennial budget in an effort to win concessions on taxes and other measures.

The action touched off a lawsuit by the legislature that claimed the veto of nearly $130 million in funding was unconstitutional. A Ramsey County District Court judge sided with lawmakers in July, leading to Dayton's appeal to the supreme court.

The governor welcomed the high court's order and said he was "ready and very willing" to begin negotiations immediately with the legislature.

Republican leaders of the House and Senate said in a statement on Friday that they will mediate in good faith, noting that their lawsuit remains undecided.

The state has been able to temporarily fund the legislature and make payments on office building and parking garage rent and bonds thanks to an order by Ramsey County Judge John Guthmann in June.

Dayton's veto raised credit concerns for the state by leaving $80.1 million of certificates of participation issued in 2014 for a Senate office facility without an appropriation for rental and debt payments next due in November and December.

After the judge ordered funding to resume, S&P on June 30 affirmed Minnesota's AA-plus rating and removed it from a watch list for a potential downgrade. (Reporting by Karen Pierog in Chicago; Editing by Matthew Lewis)