The currency has been battered this year on worries that Ankara's push to purchase Russian S-400 missile defence systems could lead to sanctions from Washington.
But a source said on Monday the United States had asked Turkey to delay the delivery, scheduled for July, which could lead to an improvement in relations between the NATO allies. However, a senior Turkish official said Ankara's position had not changed.
The lira stood at 6.0100 against the dollar at 1527 GMT, some 0.75% stronger than Monday's close of 6.0550. It firmed to as much as 5.9890 earlier in the day.
The lira is supported by a positive global sentiment toward emerging market currencies as well as news regarding the postponement of the S-400 delivery, said Guillaume Tresca, senior emerging markets strategist at Credit Agricole.
"If the reports are confirmed, it means that Turkey and the US will have room to manoeuvre and discuss the issue," he said.
Separately, industrial production fell a less-than-expected 2.2% annually in March, logging its seventh consecutive month of declines after the economy tipped into recession last year. Month-on-month, it was up 2.1% on a calendar and seasonally adjusted basis, data showed.
The Treasury tapped its two-year benchmark bond at a yield of 25.31, marking a rise of nearly six percentage points since a similar issue in March.
STATE BANKS
The lira is currently down nearly 13 percent against the dollar this year, with the most recent selloff sparked by the decision to re-run mayoral elections in Istanbul.
After slipping as far as 6.2460, its weakest in more than seven months, following last week's ruling by the electoral board, the lira recovered ground as state banks sold billions of dollars to support the currency.
Turkish state banks continuously supplied foreign currency to the market on Monday and Tuesday, traders said.
Total foreign currency sales to the market on Monday amounted to $1 billion, sources told Reuters.
The government is putting pressure on all aspects of the state to try to support the lira before the Istanbul poll is re-run on June 23, said Jason Tuvey, senior emerging markets economist at Capital Economics.
"It is only so far that the banks can do this given they've already drawn down their foreign currency assets quite a lot over the past year," he said.
Last week, banks sold a total of $4.5 billion as the central bank suspended repo auctions and took additional liquidity steps.
The main share index was up 2.02% at Tuesday's close, while the banking index rose 4.05%.
Turkey's dollar-denominated sovereign bonds rose, supported by the strengthening lira. The government's 2030 bond climbed as much as 1.3 cents in the dollar while most other bonds rose between 0.2 and 0.9 cents, Tradeweb data showed.