UK PM David Cameron says he had a "constructive" phone conversation with his Spanish counterpart Mariano Rajoy over the Gibraltar border checks row.
No 10 said during the call Mr Rajoy offered to reduce the checks, which Britain's ambassador to Spain has described as "disproportionate".
But in a subsequent statement, the Spanish PM insisted the checks were "perfectly in line" with regulations.
He did not mention any offer of curbing the border checks.
No 10 is standing by its interpretation of the call.
Ten days ago Spanish authorities increased vehicle checks at the border, causing major delays for tourists and residents.
It has also reportedly mooted bringing in a new 50 euro (£43) fee on every vehicle entering or leaving the British territory.
This followed Gibraltar's decision to drop 70 concrete blocks into the sea next to its territory, which it said would create an artificial reef and encourage sea life to flourish.
Mr Cameron had called the Spanish PM to express his "serious concerns" over deteriorating diplomatic relations between the two countries, Downing Street's press office said.
UK Foreign Secretary William Hague said he too had spoken to his Spanish counterpart. "I urged the Spanish authorities to de-escalate the situation," he reported.
Gibraltar and Spain have a long-running disagreement about how best to exploit the region's marine resources.
The concrete blocks effectively prevent Spain's favoured technique, which involves raking the sea bed, a spokesman for the Foreign Office explained.
Gibraltar's chief minister Fabian Picardo has said he has no intention of removing the reef.
But on Monday he indicated that new regulations would allow "sustainable" fishing by Spanish fleets in Gibraltar's territorial waters for the first time since they were barred in 2012, the spokesman added.
Mr Hague said this showed Gibraltar's "genuine willingness to resolve the fishing dispute".
But Spanish authorities have said Gibraltar had laid the blocks "without the necessary authorisation" in "waters that are not theirs", contravening environmental laws and damaging Spain's fishing industry.
In a statement issued after the call with Mr Cameron, Mr Rajoy said he had reiterated his desire to "seek a swift solution" to the row.
But he also said he had reiterated Spain's position that the "unilateral act of installing cement blocks in Algeciras Bay was unacceptable".