Hilton said Vonage could be irreparably injured if he completely barred its use of Verizon technology. "Some question whether they could stay in business," he said.
However, the judge said Verizon would be injured if Vonage was completely free to continue infringing the patents.
A lawyer for Vonage, Roger Warin, told the court the ruling was a "slow strangling" of the company. The difference between a partial stay or a total prohibition on using the technology amounted to "cutting off oxygen or a bullet to the head," he said.
Hilton is expected to sign his order next Thursday. Vonage is then free to take the case to the U.S. Court of Appeals for the Federal Circuit, which specializes in patent cases.
U.S. equities markets were closed for the Good Friday holiday. Vonage shares closed down almost 7 percent on Thursday to $3.37 on the New York Stock Exchange ahead of the court hearing. Verizon shares rose 1 percent to $38 on the NYSE.
Rebecca Arbogast, an analyst with Stifel Nicolaus, said Hilton's order was a blow to Vonage. "If they can't get new customers (while they appeal the case), I think it's going to be tough to attract capital."
Hilton announced on March 23 that he intended to issue an injunction blocking all use of Verizon's technology, sending Vonage shares down nearly 26 percent that day.
The judge gave Vonage two weeks to try to convince him to stay the injunction. Verizon then suggested the judge allow Vonage to keep servicing its existing customers if a stay was necessary.
Earlier in March, a jury found Vonage had infringed three patents owned by Verizon. The jury said Vonage must pay $58 million, plus 5.5 percent royalties on future sales.
Vonage stock has steadily lost value since its initial public offering at $17 a share in May last year. The shares posted an all-time closing low of $3 after Hilton's March 23 hearing.