CAIRO, March 13 (Reuters) - Egypt said on Wednesday it was lifting a $10,000 limit on the amount of hard currency foreigners can bring across its borders, easing some of the controls imposed in late 2012 as its economic crisis worsened.

"Bringing foreign currency into the country is allowed for all travellers as long as they declare it in a document provided for this purpose if the amount exceeds $10,000 or its equivalent," a government statement said.

When they departed, foreigners could leave with what remained of the cash they declared on arrival, it said.

Egypt had tightened currency controls in December, worried about sharp falls in its pound currency and a rush by Egyptians to withdraw their savings from banks.

The controls included a ban on all travellers - Egyptian and foreign - from moving more than $10,000 in foreign currency in or out of the country.

Its foreign currency reserves fell to $13.5 billion at the end of February from $36 billion just before the uprising that led to the ouster of President Hosni Mubarak in February 2011.

After two years of political instability, which has driven away tourists and foreign investors, Egypt is taking steps to lower its budget deficit and secure a $4.8 billion loan from the International Monetary Fund.

Analysts say Egypt should tap emergency IMF funding to prevent a full-blown economic crisis but the cabinet rejected that idea on Tuesday.

Egypt will also increase a departure tax for foreigners from to $20 from to $15 starting on May 1, Civil Aviation Minister Wael al-Maadawi told reporters.

He said the policy of limiting the amount of cash travellers could bring into the country had been aimed at preventing people from "mobilizing the street" with money from abroad, but that it had since been reviewed. (Reporting by Asma Alsharif; Additional reporting by Alexander Dziadosz; Editing by John Stonestreet)