(Adds quotes from economist, institute)

By Jason Lange

MEXICO CITY, July 6 (Reuters) - Mexico's severe recession showed signs of abating in June as measures of both factory and consumer sentiment jumped from a month earlier, data showed on Monday.

The Mexican Institute of Finance Executives, or IMEF, said its index on the manufacturing outlook climbed to its best reading since October, though it still pointed to future contractions.

"This suggests that the contraction in manufacturing activity is moderating," the IMEF said in a statement.

And Mexico's consumer confidence index MXCONC=ECI rose to 81.0 in June, the highest reading since January, after hitting a record low of 78.3 points in May.

Mexico is mired in its worst recession since at least the Tequila Crisis of the mid-1990s because the U.S. downturn has hit demand for its exports and caused hundreds of thousands of layoffs. Rising unemployment has hit consumer spending, making the recession more severe.

Both readings on Monday mirrored some recent improvement in the outlook for the U.S. economy. But while bolstering the view that Mexico's economy is pulling out of freefall, they still suggest there are more tough times ahead.

"We're still not talking about a recovery but at least the worst is behind us," said Rafael Camarena, an economist at Santander in Mexico City.