* EM stocks rebound as India shares steady

* Rand weakens as political uncertainty weighs

* Mexican peso rebounds after hitting 7-month lows

June 5 (Reuters) - Emerging market stocks rebounded on Wednesday, aided by stabilising Indian equity markets and softer-than-expected U.S. economic data that lifted expectations of an interest rate cut from the Federal Reserve.

The MSCI's EM equities index gained 1.04%, with India's main stock indexes rising more than 3% after having logged declines of nearly 6% on Tuesday.

Local markets were knocked lower by concerns about policy continuity after Indian Prime Minister Narendra Modi's alliance looked headed for a narrow majority in the country's 543-member parliament.

"This does not derail the top-down investment case, predicated on political stability, market-friendly policies and high headline economic growth," said Hasnain Malik, head of equity research at Dubai-based Tellimer Research.

"The election result has increased the risk of a populist tilt in fiscal policy in the short-term, but it may reduce the risk of divisive social policies and constitutional change in the long-term."

The Indian rupee ticked up to 83.36 per dollar, aided by likely intervention from the central bank after the currency slumped the most in over a year in the previous session.

Overall, EM currencies were mixed and stocks rose after data on Tuesday showed that U.S. job openings fell more than expected in April, raising bets that the U.S. central bank will begin cutting rates. This week's main economic release will be jobs data for May, due on Friday, which could give fresh hints on the Fed's easing plans.

The Mexican peso rebounded 1.2% to 17.64 per dollar after hitting a more-than-seven-month low of 18.19 on Tuesday after a strong election victory for Mexico's ruling party over the weekend sparked concerns about disputed constitutional reforms.

The Turkish lira steadied after touching near seven-week lows on Tuesday when Turkey's central bank head said it could consider decreasing the ratio of foreign exchange revenues that exporters are required to sell to the bank.

Turkey is also looking to impose a transaction tax on purchasing and selling stocks and crypto assets.

The South African rand edged lower for a second day as focus remained on which coalition partner the African National Congress (ANC) would choose after last week's election saw it lose its majority. The ANC is set to hold high-stakes internal discussions on Wednesday as coalition talks get underway.

Zambia's finance ministry said on Tuesday that holders of $3 billion of its international bonds had approved a bond restructuring proposal. June 11 is the expected settlement date, which will allow the new bonds that will be issued as part of the restructuring to start trading.

HIGHLIGHTS:

** Pakistan keen to access Chinese capital markets, says finance minister

** Indonesia c.bank to continue intervention to stabilise rupiah

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(Reporting by Sruthi Shankar in Bengaluru; Editing by Ravi Prakash Kumar)