In the last years, great efforts have been made to power scale single-mode fiber amplifiers at 1.5μm. In this context, the advantages of Er:Yb co-doped fibers as active media have been widely accepted even though their limitation due to Yb-band ASE are well known. To overcome this limitation the novel technique of off-resonant pumping (e.g. at 940nm) has demonstrated to be effective in cladding-pumped amplifiers. However, the absorption cross-section of Er:Yb fibers at these wavelengths requires a long piece of fiber to achieve high pump power absorption. This is usually an issue in single-frequency systems, where high power levels in a large interaction length reduce the threshold of non-linearities. Nonetheless, the off-resonant technique has not been yet investigated in core-pumped systems because of the low power of single-mode pump sources at 940nm. In addition, the wavelengths longer than 980nm as main pump wavelength are neither sufficiently investigated. In this work we study the viability of the off-resonant pumping technique in purely single-mode systems core-pumped at 1018nm. A 6μm core Er:Yb fiber is core-pumped with a previously generated 1018nm signal and seeded with a single-frequency signal at 1.5μm. The output signal was scaled up to >3.2W before the onset of a significant amount of ASE in the 1μm band occurred. The optical efficiency was 30\%. This work represents a proof of principle of a fiber amplifier core-pumped off-resonantly for single-frequency and purely single-mode applications.