Washington’s probe into the alleged rigging of the $13 trillion US Treasurys market by Wall Street banks has narrowed its focus to a handful of firms — including Goldman Sachs, The Post has learned.

In addition, European authorities have opened their own investigation into possible Treasurys bid-rigging, sources said.

Investigators in the fraud division of the Justice Department have obtained chats and emails from Goldman that appear to implicate the company in manipulating the price of Treasury bonds, according to two sources familiar with the investigation.

Those chats and emails are being analyzed to determine if traders at other banks could be involved with any possible bid-rigging of US government debt, those two people said.

The identities of any traders in investigators’ cross hairs couldn’t be learned.

Goldman is said to be cooperating with the probe, one person said.

In June, The Post reported exclusively that Justice was in the early stages of investigating banks for rigging the price of Treasurys, the largest and most easily tradeable asset in the world.

Goldman is one of about 22 financial institutions that have been probed for any evidence that they may have manipulated Treasury auctions — a secretive process where banks and other financial services companies bid on the price of government debt, sources said.

Justice is also looking into whether there was price-rigging in the secondary market for Treasurys, where debt is sold at a premium, sources added. It’s unclear if investigators have yet found any improprieties or criminality.

Goldman, run by Chief Executive Lloyd Blankfein, is a major player in US government bond trading, and regularly submits bids for auctions.

In November, Goldman disclosed in a regulatory document that it was being probed for possible manipulation of government bond prices. Michael DuVally, a Goldman spokesman, declined to comment further.

Meanwhile, the European Commission, the law enforcement arm of the European Union, has opened its own investigation, joining Justice, the Securities and Exchange Commission, the Commodity Futures Trading Commission, and the New York Department of Financial Services, according to two sources.

The rigging investigation is the biggest scandal to hit the quiet but crucial Treasurys market since 1990 when Paul Mozer, a former Salomon Brothers partner, illegally cornered the government debt market. Mozer’s actions are known to readers of Michael Lewis’ “Liar’s Poker.”

Traders are thought to have rigged the market in two possible ways: by agreeing beforehand to keep bond prices higher than normal in order to boost profits in other positions that depend on higher rates, similar to how banks rigged the London-based Libor rate.

Banks also could have colluded to keep prices lower than normal to sell them at a higher price — and score a bigger spread — to their clients, who agreed to pay a fixed amount beforehand.

A Justice Department spokesman didn’t return an email seeking comment, while EC spokesman Ricardo Cardoso declined to comment.