"United States Maritime Alliance ... refuses to address a half-century of wage subjugation," the union said in a statement.
The United States Maritime Alliance, known as USMX, represents employers of the east and Gulf Coast longshore industry.
USMX did not immediately comment.
If union members walk off the job at ports stretching from Maine to Texas, it would be the first coast-wide ILA strike since 1977, affecting ports that handle about half the country's ocean shipping.
A source said no negotiations were taking place on Sunday and none are currently planned before the midnight Monday deadline.
The union said previously the strike would not affect military cargo shipments or cruise ship traffic.
The White House did not immediately comment on the union's statement.
Earlier on Sunday, US President Joe Biden said he did not intend to intervene to prevent a walkout if dock workers failed to secure a new contract by an October 1 deadline.
"It's collective bargaining. I don't believe in Taft-Hartley," he told reporters.
Presidents can intervene in labour disputes that threaten national security or safety by imposing an 80-day cooling-off period under the federal Taft-Hartley Act.
Reuters first reported on September 17 that Biden did not plan to invoke the Taft-Hartley provision, citing a White House official.
A strike could stop the flow of everything from food to cars at major ports - in a dispute that could jeopardise jobs and stoke inflation weeks ahead of the US presidential election.
Business Roundtable, which represents major US business leaders, said it was "deeply concerned about the potential strike at the east coast and Gulf Coast ports".
The group warned a labour stoppage could cost the US economy billions of dollars daily "hurting American businesses, workers and consumers across the country. We urge both sides to come to an agreement before Monday night's deadline."
For months, the union has threatened to shut down the 36 ports it covers if employers like container ship operator Maersk and its APM Terminals North America do not deliver significant wage increases and stop terminal automation projects.
The dispute is worrying businesses that rely on ocean shipping to export their wares or secure crucial imports.
On Friday, US administration officials met with the United States Maritime Alliance employer group to directly convey "that they need to be at the table and negotiating in good faith fairly and quickly" - a message it delivered earlier to the ILA.
The USMX employer group has accused the ILA of refusing to negotiate.
