The simulated impact of the Atlantic meridional overturning circulation (AMOC) on the low-frequency variability of the Arctic surface air temperature (SAT) and sea ice extent is studied with a 1000-year-long segment of a control simulation of the Geophysical Fluid Dynamics Laboratory Climate Model version 2.1. The simulated AMOC variations in the control simulation are found to be significantly anticorrelated with the Arctic sea ice extent anomalies and significantly correlated with the Arctic SAT anomalies on decadal time scales in the Atlantic sector of the Arctic. The maximum anticorrelation with the Arctic sea ice extent and the maximum correlation with the Arctic SAT occur when the AMOC index leads by one year. An intensification of the AMOC is associated with a sea ice decline in the Labrador, Greenland, and Barents Seas in the control simulation, with the largest change occurring in winter. The recent declining trend in the satellite-observed sea ice extent also shows a similar pattern in the Atlantic sector of the Arctic in the winter, suggesting the possibility of a role of the AMOC in the recent Arctic sea ice decline in addition to anthropogenic greenhouse-gas-induced warming. However, in the summer, the simulated sea ice response to the AMOC in the Pacific sector of the Arctic is much weaker than the observed declining trend, indicating a stronger role for other climate forcings or variability in the recently observed summer sea ice decline in the Chukchi, Beaufort, East Siberian, and Laptev Seas.