More than 500 Port of Liverpool staff had already started two weeks of industrial action 10 days ago.
Control room staff including senior operators will join port operatives and engineers in an additional week-long strike of nearly 600 workers between 11 and 17 October.
Peel Ports Group said a “significant” 8.3% offer had been rejected.
Workers said the pay offer amounted to a real-terms pay cut as inflation continues to rise in the cost of living crisis.
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Unite is also in dispute with Peel over a failure to honour a pay agreement made last year.
The union said the company had not undertaken a promised pay review, the last of which happened in 1995, and had failed to deliver on an agreement to improve rotas.
Unite general secretary Sharon Graham said: “Our members will not back down and neither will Unite.
“Peel needs to keep its previous pay promises and put forward a proper pay rise now”.
Steven Gerrard, Unite’s national coordinator for free ports, said the disruption caused to the port and its supply lines was “entirely the fault” of Peel Ports.
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“The company can afford to put forward an offer our members can accept and must do so,” he said.
Peel Ports said: “We have offered a very significant 8.3% pay package, and a £750 one off-payment, which would ensure the staff involved are among the best-paid in the industry, so it’s disappointing that further, damaging strike action has been scheduled.
“We can assure all our non-container customers that their port operations will continue as normal during this period.”
The Port of Liverpool operates two container terminals, the Royal Seaforth Container Terminal and Liverpool2.
Source: BBC
