Ivanov and Bolton held "constructive" talks
President Bush's remarks triggered fresh diplomatic activity between Moscow and Washington, but brought no official response from the Kremlin.
Correspondents are interpreting the lack of comment from Moscow as a signal that Russia's position on ABM remains unchanged.
The American Under-Secretary of State, John Bolton, who was in Moscow for talks on the ABM, delayed his departure to hold unscheduled discussions with Russian Foreign Minister Igor Ivanov.
Mr Bush on Thursday insisted on that the US would withdraw from the treaty, at a time of its choosing, but he promised to continue talks with Moscow and US allies on the issue.
Constructive dialogue
Friday's talks between the Russian foreign minister and Mr Bolton were described as a "constructive dialogue" by Mr Ivanov.
However, Mr Ivanov gave no specific response to the US president's comments.
Russia says the ABM treaty, signed in 1972, is still the cornerstone of global security, and America's plans for a missile defence system risks sparking a new arms race.
Pressure on Moscow
BBC Moscow correspondent Caroline Wyatt says Mr Bush's statement put further pressure on Russia to soften its stance, yet the Kremlin shows no sign of doing so, and the US president's blunt statement leaves little room for manoeuvre.
However, the diplomacy is expected to continue in the run up to Mr Bush's next meeting with the Russian President Vladimir Putin first in China this October and then at Mr Bush's ranch in Texas the following month.
Opposition
Russia is bitterly opposed to the US plan to scrap or sideline the ABM in order to establish a missile shield.
China also opposes the plan, and several key US allies worry it could spark a new arms race.
But time appeared to be running short for Mr Putin to agree to scrap or modify the accord, with US officials saying it is a matter of "months, not years" before efforts to develop a missile shield will infringe on the treaty.
And the accord, the cornerstone of arms control efforts by the United States and then-Soviet Union, calls for six-months' notice prior to withdrawal.
Rogue state fears
Washington says the shield is necessary to protect it from purported threats coming from so-called "rogue states" such as North Korea and Iraq.
Russia has reaffirmed its adherence to the treaty, saying that present consultations on possible cuts in nuclear arsenals are conditional on the ABM treaty being maintained in its present form.
Senior Russian military officials have stated that specific talks with Washington on the missile defence issue are unlikely before next year.
The 1972 ABM treaty, signed by the US and the USSR, forbids the development of a nationwide defence system.
New head of army
In another development, President Bush has nominated a new head for the US Army.
General Richard Myers, a former head of the Air Force, is being promoted to chairman of the Joint Chiefs of Staff from his current position as vice chairman.
Mr Bush said the general was the best placed man to meet the threats of the future.
Correspondents say the appointment of General Myers, who has been at the forefront of space-based military planning, confirms the president's commitment to a controversial missile defence system.