Men's Wearhouse said it offered to acquire all outstanding shares of Jos. A. Bank for $57.50 per share, higher than its November offer of $55.
The tender offer, the latest move in a long battle between the two retailers intent on playing the lead role in creating a combined entity, expires on March 28.
Men's Wearhouse also said it intended to nominate two independent directors to Jos. A. Bank's board.
(Read more: Jos. A Bank rejects Men's Wearhouse bid)
"Although we have made clear our strong preference to work collaboratively with Jos. A. Bank to realize the benefits of this transaction, we are committed to this combination and, accordingly, we are taking our offer directly to shareholders," Men's Wearhouse Chief Executive Doug Ewert said in a statement.
Jos. A. Bank lowered the trigger for its shareholder rights plan on Friday to 10 percent from 20 percent, making it tougher for Men's Wearhouse to pursue a bid.
Men's Wearhouse, which is under pressure from activist shareholders to merge, said on Monday it would nominate John Bowlin, former chief executive of Miller Brewing Co, and Arthur Reiner, a former executive of Macy's Inc (M.N), to Jos. A. Bank's board.
(Read more: Activist wants to dress down Men's Wearhouse board)
Men's Wearhouse rejected in November an offer from the smaller rival and adopted a poison pill.