But Mexican billionaire Carlos Slim's group, which said it now owns 29.77 percent of KPN, reiterated it still plans to go ahead with its proposed 7.2 billion euros ($9.65 billion) bid in cash for the remaining shares in the Dutch group.
KPN, Telefonica and America Movil said on Monday that the Spanish telecom firm had agreed to pay the equivalent of 8.55 billion euros ($11.46 billion) for E-Plus, compared with its earlier offer of 8.1 billion euros.
(Read more: Why Carlos Slim's KPN bid may be all about Germany)
KPN will still receive 5 billion euros in cash for E-Plus and will have a bigger stake in Telefónica's German business of 20.5 percent, compared with the 17.6 percent previously agreed.
The improved agreed terms for the E-Plus deal remove uncertainty. People close to the matter said at the time that Slim's company viewed the offer as too low and fraught with regulatory risks.
But KPN has so far not welcomed Slim's move to increase his grip over the Dutch group, and an independent foundation that has the potential to block KPN's takeover has expressed concern over that proposed bid.
(Read more: Billionaire Carlos Slim makes $9.6 billion KPN bid)
In a statement on Monday, América Móvil said it believed that by acquiring a majority stake in KPN, both companies could benefit from greater operational co-operation and co-ordination.
"By achieving majority ownership, AMX believes it will be able to support KPN to a greater extent with its investment plans in a rapidly changing European environment," the Mexican group said in a statement.