WASHINGTON — President Biden on Friday asked Congress for another nearly $10 billion to fix the country’s Border immigration system — with $1.4 billion carved out for struggling state and local governments.

New York, though, was left guessing how much it would even get to help ease the billions of dollars the city is on the hook for to care and house the more than 130,000 migrants who have come through its care.

The request was buried in a larger nearly $106 billion spending request headlined by $61.4 billion for Ukraine and $14.3 billion for Israel.

A White House fact sheet said that $13.6 billion would go to address the border with $1.4 billion of those funds going toward “shelter and services for migrants released from DHS custody,” but the administration did not immediately respond to The Post’s request for comment on how much of the aid would flow to the Big Apple.

In August, the Biden administration pushed for a nearly $4 billion supplemental request from Congress.

New York City Mayor Eric Adams and New York Gov. Kathy Hochul have been critical of Biden’s management of record-breaking illegal immigration along the US-Mexico border — and have pleaded for cash to offset what Adams has said could be a $12 billion cost to New York City.

Biden snubbed Hochul in August when she visited the White House to discuss migration’s impact.

White House press secretary Karine Jean-Pierre said that Biden couldn’t find time to meet with Hochul because he “has a lot on his plate” — even though he found time the same day for a non-time-sensitive meeting with Sen. Bernie Sanders (I-Vt.).

This cold shoulder for fellow Democrats comes as Adams said the migrant cost is battering the Big Apples budget so badly he had to call for 15% cuts to the majority of city agencies with caps on discretionary spending.

It’s unclear if Congress will pass the massive spending bill in one piece due to growing skepticism of Ukraine war aid after legislators approved $113 billion for Kyiv earlier in Russia’s 20-month invasion.

The budget request includes other proposed funds to address the border, including $1.9 billion for the Department of Health and Human Services to “support eligible arrivals and unaccompanied children,” $1.6 billion for more Border Patrol Agents and asylum officers, $1.4 billion for new immigration judges, $1.2 billion for fentanyl-screening equipment, $1.3 billion to support new “legal pathways” for migrants and a much smaller $40 million boost in funding for deportations.

Biden has presided over a record-breaking wave of illegal immigration, which he has attributed to economic factors and insecurity across Latin America.

His detractors blame his more welcoming rhetoric and the fact that a large share of illegal entrants are allowed to remain to await asylum rulings.

Fiscal 2023, which ended Sept. 30, is expected to set an annual record for Southwest border apprehensions — with 2.2 million arrests in the first 11 months of data.

A record-breaking 2.38 million apprehensions were logged in fiscal 2022.

Texas Republican Gov. Greg Abbott has protested Biden’s release of migrants who illegally crossed the border as well as anti-deportation “sanctuary” policies of Democratic jurisdictions by sending thousands on buses to New York City and other major cities.

As of this month, Abbott’s government had sent 18,500 migrants from the border to New York City since April 2022.

A local law obligates the city to provide migrants with free housing, making the burden on local officials greater than in other regions.

Asylum seekers are eligible for work permits after as little as 180 days after arriving — a process that Adams has asked the Biden administration to shorten to alleviate costs to the city.