  In 2019, Letzter confirmed a conjecture of Balogh, Bar\'at, Gerbner,
Gy\'arf\'as and S\'ark\"ozy, proving that every large $2$-edge-coloured graph
$G$ on $n$ vertices with minimum degree at least $3n/4$ can be partitioned into
two monochromatic cycles of different colours. Here, we propose a weaker
condition on the degree sequence of $G$ to also guarantee such a partition and
prove an approximate version. This resembles a similar generalisation to an
Ore-type condition achieved by Bar\'at and S\'ark\"ozy.
  Continuing work by Allen, B\"ottcher, Lang, Skokan and Stein, we also show
that if $\operatorname{deg}(u) + \operatorname{deg}(v) \geq 4n/3 + o(n)$ holds
for all non-adjacent vertices $u,v \in V(G)$, then all but $o(n)$ vertices can
be partitioned into three monochromatic cycles.
