We investigate an extended cosmological model motivated by the asymptotic safety of gravitational field theory, in which the matter and radiation densities and the cosmological constant receive a correction parametrized by the parameters δ
G
and δ
Λ
, leading to that both the evolutions of the matter and radiation densities and the cosmological constant slightly deviate from the standard forms. Here we explain this model as a scenario of vacuum energy interacting with matter and radiation. We consider two cases of the model: (i) Λ̃CDM with one additional free parameter δ
G
, with δ
G
and δ
Λ
related by a low-redshift limit relation and (ii) eΛ̃CDM with two additional free parameters δ
G
and δ
Λ
that are independent of each other. We use two data combinations, CMB+BAO+SN (CBS) and CMB+BAO+SN+H
0 (CBSH), to constrain the models. We find that, in the case of using the CBS data, neither Λ̃CDM nor eΛ̃CDM can effectively alleviate the H
0 tension. However, it is found that using the CBSH data the H
0 tension can be greatly relieved by the
models. In particular, in the case of eΛ̃CDM, the H
0 tension can be resolved to 0.71σ. We conclude that as an interacting dark energy model, Λ̃CDM is much better than Λ(t)CDM in the sense of both relieving the H
0 tension and fitting to the current observational data.