By Herbert Lash and Harry Robertson

NEW YORK/LONDON (Reuters) -The euro strengthened as the dollar slid on Tuesday in response to a sharp drop in Treasury yields on the back of further dovish comments by Federal Reserve officials, as well as the prospect of stimulus from China.

The benchmark 10-year Treasury note tumbled to a day low of 4.618% from Monday's high of 4.887% after Atlanta Fed President Raphael Bostic said the U.S. central bank does not need to increase interest rates any further.

Bostic, in the latest comments this week by Fed speakers, told the American Bankers Association that Fed policy is sufficiently restrictive and that he sees no recession ahead even as the Fed's rate hikes slow the economy and bring down inflation.

Bostic was partly responding to the outburst of violence in Israel and Gaza, said Joseph Trevisani, senior analyst at FXStreet in New York.

"You're looking at the typical and standard and historically repeated reaction of the Fed to a crisis that (would) lower rates if things get ugly in the Middle East," he said.

"You can pretty much count on the Fed taking that into its world view and that's only going to be lower rates."

U.S. Treasuries rallied, pushing two-year yields to their lowest in a month, as safe-haven demand was driven by the ongoing Mideast bloodshed and dovish Fed comments.

The euro rose 0.3% against the dollar to $1.0604, while the dollar index, a measure of the U.S. currency against six others, slid about 0.19% to 105.75, well below last week's 11-month high of 107.34, after touching the lowest level this month.

"The focus on term yields and term premiums is going be a key issue for the U.S. dollar because it does suggest that maybe the Fed doesn't have to go any more," said Shaun Osborne, chief FX strategist at Scotiabank in Toronto.

"These are all things that are going to check the dollar's advance. Whether we see any sort of significant decline at this point, it's hard to say given where yields are," he said.

Traders awaited the release on Wednesday of minutes from the Fed's last policy move as well as key U.S. inflation data on Thursday. Investors also are keeping a close eye on the conflict between Israel and the Palestinian Islamist group Hamas, though the initial safe-haven purchase of the dollar has stopped.

Bloomberg reported that China is weighing the issuance of at least 1 trillion yuan ($137.1 billion) of additional sovereign debt for spending to boost its struggling economy. Analysts said this helped currencies such as the euro, which are more exposed to global growth.