Vodafone has called on Hutchison Whampoa, Three's parent company, to scrap a network-sharing joint venture with EE.
Vittorio Colao, Chief Executive at Vodafone, said the link-up between Three and EE should end if Three's intended takeover of O2 goes ahead.
He highlighted Vodafone's existing network-sharing agreement with O2, which he claimed would make it difficult for Three to continue working with EE, which is becoming part of BT.
"O2 has contractual obligations on network sharing with us. They should respect the obligations. Clearly [Three] had had an agreement with EE," Mr Colao stated.
"The two are not compatible, so they should look at that, otherwise you create another concentration."
However, Olaf Swantee, Chief Executive of EE, described his company's contract with Three as "a long-term relationship".
He noted that EE and Three mainly share 3G coverage, rather than premium super-fast 4G services.