(Adds details and background from paragraph 2 onwards) Oct 2...

(Adds details and background from paragraph 2 onwards)

Oct 2 (Reuters) - Australian billionaire Gina Rinehart's Hancock Prospecting increased its stake in lithium miner Liontown Resources (LTR) , the company said, moving it closer to being able to block a $4.3 billion bid by U.S.-based Albemarle ALB.N for Liontown.

Hancock said on Friday it raised its stake from 10.7% last month to 12.4%, paying no more than A$3.00 per additional share. Hancock would be able to block the Albemarle deal with a 15% position.

Last month, Liontown accepted Albemarle's revised $4.3 billion bid, or A$3 a share. Albemarle, the world's largest lithium producer, is seeking to secure supplies of the key electric vehicle battery metal. The offer is part of a surge of interest in Australian lithium assets amid the clean energy transition.

Hancock said last month it may seek a position on Liontown's board and could help the company bring its lithium resources to production.

Last week, Liontown raised its capital cost to first production estimate for its Kathleen Valley lithium project by 6% to A$951 million ($611.4 million) but confirmed it would meet its target for production to start in mid-2024.

Hancock said the increased cost estimate underscored the project's "significant execution, operational ramp-up and market risks." Hancock said that the actual capital cost for the project could be in excess of A$1 billion, factoring in inflation over time.

Rinehart, Australia's richest person, owns shares in lithium companies such as Patriot Battery Metals PMET.V and Delta Lithium (DLI) , in line with her recent focus on the sector. ($1 = 1.5555 Australian dollars)