By Gertrude Chavez-Dreyfuss

NEW YORK (Reuters) - Sterling recovered from a two-month low against the euro on Thursday and rose versus the dollar, extending gains after British police said Jo Cox, a lawmaker for Britain's opposition Labour Party, had died after being attacked earlier in the day.

The yen, meanwhile, jumped to its highest in more than three years against the euro and its strongest in nearly two years versus the dollar on Thursday after the Bank of Japan held off from further easing monetary policy and the Federal Reserve struck a cautious tone on the U.S. economy.

The safe-haven yen also hit a three-year peak against sterling <GBPJPY=> and a four-year high versus the Australian dollar <AUDJPY=> as investors shunned higher-yielding but riskier currencies ahead of next week's referendum to determine whether Britain will stay in the European Union.

With polls showing the "Leave" camp pushing ahead, few had expected the BOJ to risk easing policy before the June 23 vote.

In the UK, the pound drew support in the wake of Cox's death. The 41-year-old British lawmaker was one of the members of parliament advocating for Britain to remain in the EU, an issue that will be decided in a referendum next week. Cox was attacked as she prepared to hold a meeting with constituents in Birstall near Leeds.

Brian Jacobsen, chief portfolio strategist at Wells Fargo Funds Management in Menomonee Falls, Wisconsin, said an event like this matters ahead of the referendum, although he was not sure whether it is enough to shift the odds to favor the "Remain" camp.

EU referendum campaigns were suspended on Thursday following Cox's killing.

In late trading, the euro was off 0.2 percent against sterling to 79.05 pence <EURGBP=>, after hitting a two-month peak of 79.94.

Sterling gained 0.2 percent against the dollar to $1.4209 <GBP=> after trading lower for most of the session.

In Japan, the BOJ maintained its massive asset buying program at its two-day rate review that ended on Thursday, pledging to increase base money at an annual pace of 80 trillion yen ($753 billion).

In late trading, the dollar was down 1.6 percent to 104.34 yen <JPY=>. It hit a 22-month low earlier in the session below 104, and kept the market on alert for possible Japan intervention to rein in the yen's recent strength. The euro dropped 1.8 percent against the yen to 117.25 yen <EURJPY=>, after earlier hitting a 3-1/2-year trough at 115.84.

(Reporting by Gertrude Chavez-Dreyfuss; Additional reporting by Dion Rabouin, Karen Brettell and Rodrigo Campos; Editing by Nick Zieminski and James Dalgleish)